Central Series for Groups with Action and Leibniz Algebras

abstract:
The notion of central series for groups with action on itself is introduced.
An analogue of Witt's construction is given for such groups. A certain condition
is found for the action and the corresponding category is defined. It is proved
that the above construction defines a functor from this category to the category
of Lie-Leibniz algebras and in particular to Leibniz algebras; also the
restriction of this functor on the category of groups leads us to Lie algebras
and gives the result of Witt.